On the fractional Schrödinger problem with non‐symmetric potential

We study the semilinear equation where 0 < s < 1, , V(x) is a sufficiently smooth non‐symmetric potential with , and ? > 0 is a small number. Letting U be the radial ground state of (?Δ)^sU + U ? U^p=0 in , we build solutions of the form for points ?_j,j = 1,?,m, using a Lyapunov–Schmidt variational reduction. Copyright © 2014 John Wiley & Sons, Ltd.     

Continuous random walks and fractional powers of operators

We derive a probabilistic representation for the Fourier symbols of the generators of some stable processes. This short paper represents a bridge between probabilists and researchers working in PDE?s.     

Three solutions for a class of quasilinear elliptic equation involving the p − q‐Laplace operator

The existence of at least three weak solutions is established for a class of quasilinear elliptic equation involving the p ? q‐Laplace operator with Dirichlet boundary condition. The technical approach is mainly on the basis of a three critical points theorem due to Ricceri. Copyright © 2013 John Wiley & Sons, Ltd.     

On Spectral Integral Variations of Graphs

Let G be a general graph. The spectrum S ( G ) of G is defined to be the spectrum of its Laplacian matrix. Let G + e be the graph obtained from G by adding an edge or a loop e . We study in this paper when the spectral variation between G and G + e is integral and obtain some equivalent conditions, through which a new Laplacian integral graph can be constructed from a known Laplacian integral graph by adding an edge.     

LAMOST-DR1中激变变星光谱的数据挖掘研究

LAMOST-DR1是郭守敬望远镜正式巡天发布的首批数据,其数量超过目前世界上所有已知恒星巡天项目的光谱总数。这为进一步扩大特殊和稀少天体如激变变星的数量提供了样本,同时也对天文数据处理方法和技术提出了更高的要求。针对LAMOST的数据特点,提出一种能够在海量天体光谱中自动、快速发现激变变星的方法。该方法使用拉普拉斯特征映射对天体光谱进行降维和重构。结果表明不同类别的天体光谱在拉普拉斯空间中能够得到较明显的区分。在使用粒子群算法对神经网络的参数进行优化后,对LAMOST-DR1的全部数据进行了自动识别。实验共发现了7个激变变星,经过证认,其中2个是矮新星,2个是类新星,1个是高度极化的武仙座AM型。这些光谱,补充了现有的激变变星光谱库。本文验证了拉普拉斯特征映射对天体光谱进行特征提取的有效性,为高维光谱进行降维提供了另一途径。在郭守敬望远镜正式发布的数据中寻找激变变星的首次尝试,实验结果表明该自动化的方法鲁棒性好,速度快,准确率高。该方法也可用于其他大型巡天望远镜的海量光谱处理。     

Collapsing of connected sums and the eigenvalues of the Laplacian

We study the behavior of the eigenvalues of the Laplacian acting on functions when one side of a connected sum of two closed Riemannian manifolds collapses to a point. We prove that the eigenvalues converge to those of the limit space, by using the method of Anné and Colbois. From this, we obtain a gluing theorem for the eigenvalues.     

Detail enhancement of blurred infrared images based on frequency extrapolation

A novel algorithm for enhancing the details of the blurred infrared images based on frequency extrapolation has been raised in this paper. Unlike other researchers’ work, this algorithm mainly focuses on how to predict the higher frequency information based on the Laplacian pyramid separation of the blurred image. This algorithm uses the first level of the high frequency component of the pyramid of the blurred image to reverse-generate a higher, non-existing frequency component, and adds back to the histogram equalized input blurred image. A simple nonlinear operator is used to analyze the extracted first level high frequency component of the pyramid. Two critical parameters are participated in the calculation known as the clipping parameter C and the scaling parameter S. The detailed analysis of how these two parameters work during the procedure is figure demonstrated in this paper. The blurred image will become clear, and the detail will be enhanced due to the added higher frequency information. This algorithm has the advantages of computational simplicity and great performance, and it can definitely be deployed in the real-time industrial applications. We have done lots of experiments and gave illustrations of the algorithm’s performance in this paper to convince its effectiveness.     

催化裂化催化剂有机硫氮转化机理量子化学分析

国家环保法规的日益严格使得对催化裂化（FCC）再生烟气提出了更高的管控要求,再生烟气中污染物组成复杂且转化机制尚不清楚,迫切需要深入理解FCC待生催化剂中污染物的转化机理。对待生催化剂中有机硫和有机氮进行合理简化,选取合适的模型化合物,采用Gassian09软件,在B3LYP/def2-TZVP级别下,对模型化合物进行几何优化得到最稳定构型,并进行振动分析。利用Multiwfn多功能波函数分析仪对优化后模型化合物进行Laplacian键级分析（LBO）,通过LBO键级计算结果,得到自由基在再生过程中的详细转化机理。结果表明,含氮化合物中C—N键和含硫化合物中C—S键与C—C键相比均较弱,在催化剂再生过程中会优先发生断裂,生成不同的含氮（NH3、HCN）、含硫（H2S、COS）中间体,随后进一步与氧气反应生成相应的NOx、SOx。     

Scaling coupling of reflecting Brownian motions and the hot spots problem

We introduce a new type of coupling of reflecting Brownian motions in smooth planar domains, called scaling coupling. We apply this to obtain monotonicity properties of antisymmetric second Neumann eigenfunctions of convex planar domains with one line of symmetry. In particular, this gives the proof of the hot spots conjecture for some known types of domains and some new ones.

     

Perron components and algebraic connectivity for weighted graphs

The algebraic connectivity of a connected graph is the second-smallest eigenvalue of its Laplacian matrix, and a remarkable result of Fiedler gives information on the structure of the eigenvectors associated with that eigenvalue. In this paper, we introduce the notion of a perron component at a vertex in a weighted graph, and show how the structure of the eigenvectors associated with the algebraic connectivity can be understood in terms of perron components. This leads to some strengthening of Fiedler's original result, gives some insights into weighted graphs under perturbation, and allows for a discussion of weighted graphs exhibiting tree-like structure.